Decoding Hidden Complexities of Kinetic Experiments

Abstract

Time trace data obtained from single-molecule kinetic experiments such as fluorescence, ion conduction and force extension, often appear in the form of stochastic time trajectories, exhibiting complex behavior that cannot be described by a single exponential. The underlying system is usually modeled as aggregated Markov states, where each experimentally observable property comes from an aggregate of indistinguishable states, making transitions to each other via Markov process. However, such a modeling has limitations in that the underlying network topology has to be assumed in advance, and that there are many models consistent with the data. In this work, we introduce a new method of modeling such systems using a non-Markov model. In contrast to the aggregated Markov model, the new method leads to a unique dynamical model for a given time trace data. Furthermore, it is shown that the current formalism is more general than the aggregated Markov model, including the latter as a special case. We also develop an algorithm for extracting the non-Markov memory kernel from a noisy experimental data, based on the Maximum Entropy Principle, the method for the unbiased estimation. Some preliminary analysis of simulated and real experimental data will be presented.